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If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3), ...

If `sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),` then prove that `(dy)/(dx)=(x^2)/(y^2)sqrt((1-y^6)/(1-x^6))`

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We have given
`sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),`
Put `x^3 = sintheta, y^3 = sinphi`
`costheta + cosphi = a(sintheta – sinphi)`
`2cos((theta+phi)/2)cos((theta-phi)/2)=a.2cos((theta+phi)/2)sin((theta-phi)/2)`
`cot((theta-phi)/2)=a`
`(theta-phi)/2=cot^(-1)(a)`
`theta-phi=2cot^(-1)(a)`
...
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